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# Transformations and Angle Relationships

## Objective

Describe sequences of transformations between figures using rotations and other transformations.

## Common Core Standards

### Core Standards

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• 8.G.A.1.A — Lines are taken to lines, and line segments to line segments of the same length.

• 8.G.A.1.B — Angles are taken to angles of the same measure.

• 8.G.A.1.C — Parallel lines are taken to parallel lines.

• 8.G.A.2 — Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

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• 4.MD.C.6

## Criteria for Success

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1. Perform a combination of transformations, using rotations and other transformations, on a figure.
2. Describe a sequence of transformations with precision, using rotations and other transformations, between two figures (MP.6).
3. Understand that properties of transformations hold true even when there are multiple rigid transformations; for example, the side length of a polygon that is rotated and reflected is the same on the original figure and the transformed figure.

## Tips for Teachers

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#### Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problem 1 (benefits from worked example). Find more guidance on adapting our math curriculum for remote learning here.

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• Problem Set
• Student Handout Editor
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## Anchor Problems

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### Problem 1

Figure 1 is shown in the coordinate plane below.

Which figure(s) would Figure 1 map to if it were

• translated?
• reflected?
• rotated?

#### Guiding Questions

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### Problem 2

Below is a picture of two rectangles with the same length and width:

1. Show that the rectangles are congruent by finding a translation followed by a rotation that maps one of the rectangles to the other
2. Explain why the congruence of the two rectangles cannot be shown by translating Rectangle 1 to Rectangle 2.

#### Guiding Questions

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#### References

Illustrative Mathematics Congruent Rectangles

Congruent Rectangles, accessed on Oct. 13, 2017, 4:01 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

### Problem 3

Figures ${J, K, L, M, N,}$ and $P$ are shown on the coordinate plane.

Part A:

Which figure can be transformed into Figure P by a translation 2 units to the right followed by a reflection across the $x-$axis?

a.     Figure J

b.     Figure K

c.     Figure L

d.    Figure M

Part B: Which figure can be transformed into Figure L by a 90-degree rotation clockwise about the origin followed by a translation 2 units down?

a.     Figure J

b.     Figure M

c.     Figure N

d.     Figure P

#### Guiding Questions

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#### References

PARCC Released Items Math Spring Operational 2015 Grade 8 End of Year Released ItemsProblem #10

Math Spring Operational 2015 Grade 8 End of Year Released Items is made available by The Partnership for Assessment of Readiness for College and Careers (PARCC). Copyright © 2017 All Rights Reserved. Accessed Oct. 13, 2017, 4:02 p.m..

## Problem Set

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With Fishtank Plus, you can download a complete problem set and answer key for this lesson. Download Sample

The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

• Examples where students perform transformations that involve a combination or rotations and either reflections or translations to determine if two figures are congruent
• Examples where students identify coordinate points of rotated vertices; be sure to include examples of rotations around the origin and around a point on a figure
• Examples where students demonstrate understanding of properties of transformations

## Target Task

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### Problem 1

Triangle ${{ABC}}$ is rotated ${90^{\circ}}$ clockwise around the origin.

Which of the statements below are true? Select all that apply.

a.     Point ${{B'}}$ will be located at ${(1, 4)}$.

b.     Point ${{B'}}$ will be located at ${(4,1)}$.

c.     $\overline{{{B'}}C'}$ will be a vertical line.

d.     $\overline{{{B'}}C'}$ will be parallel to ${\overline{BC}}$.

e.     The area of $A'{{B'}}C'$ will be greater than the area of ${{ABC}}$, but the perimeters will be the same.

f.     Both the areas and perimeters of the original and the rotated figures will be the same.

### Problem 2

Describe how you can use transformations to show that the two figures below are congruent.

### Mastery Response

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